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Information Sciences Letters

Information Sciences Letters

Abstract

In this paper, a nonlinear free vibration of strongly nonlinear oscillators is studied. To this end, we propose a novel technique using He’s frequency-amplitude formulation and He’s energy balance method called iteration perturbation procedure. A novel technique called iteration perturbation procedure and variational iteration method are presented to obtain the relationship between amplitude and angular frequency. The obtained results are compared with the numerical solution obtained by using the Runge–Kutta method and shown in graphs indicating the effectiveness and convenience of the analytical approximate solutions. These approaches are very effective and simple and with only one iteration leads to high accuracy of the solutions. It is predicted that those methods can be found wide applications in engineering problems, as indicated in this paper.

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